The effects of a curved continuum

In the above spectral fitting, we have assumed that the underlying X-ray continuum is strictly a power-law form. One might think that this would be a good assumption, since the observed band (0.5-10keV) is much higher than the likely energy of the seed photons for the thermal Comptonisation (tens of eV) but much lower than the electron energy of a typical disk corona (100-200keV). However, we must acknowledge the possibility that MCG$-$6-30-15 may be unusual in possessing a particularly cool corona. In this section, we assess the effect that the resulting continuum curvature would have on the inferred X-ray reflection as a function of radius in the disk.

For this study, we examine the 2-10keV EPIC-pn data supplemented by the 3-15keV RXTE-PCA data. Adding the 0.5-2keV EPIC-pn data complicates the spectral fitting (since one must account for the soft X-ray absorption/emission) without improving the constraints. The major limitation in the study of a curved continuum is the lack of readily available reflection models that can handle non-power law input spectra. We use the compTT model (Titarchuk 1994) in XSPEC to describe the continuum resulting from thermal Comptonisation. The seed photons are assumed to be characterized by a Wien spectrum with $kT=50$eV (typical of the optically-thick part of AGN disk). The temperature $T$ and optical depth $\tau$ of the corona are left as free parameters. We then employ the reflect model (Magdziarz & Zdziarski 1995) in XSPEC to model the Compton reflection of this continuum spectrum from the disk surface. A narrow Gaussian emission line with a rest-frame energy in the range 6.40-6.97keV is added to model the iron fluorescence line, and the whole spectrum is convolved with the laor (Laor 1991) kernel to describe the Doppler and gravitational redshift effects associated with the accretion disk.

This procedure constrains the temperature of the corona to be greater than $kT\sim 5.2$keV; for coronal temperatures exceeding this, there is an almost perfect cancellation between spectral curvatures resulting from different coronal temperatures, reflection fractions and relativistic smearings. However, for all allowable coronal temperatures, a very steep emissivity index is required, $\beta>3.9$. Freezing the emissivity index to be $\beta=3$ resulted in a worsening of the goodness of fit parameter by $\Delta\chi^2=400$. Thus, our principal result is secure against the continuum curvature introduced by standard thermal Comptonisation models.